If `x_(n)gt1` for all `n in N`, then the minimum value of the expression
`log_(x_(2))x_(1)+log_(x_(3))x_(2)+...+log_(x_(n))x_(n-1)+log_(x_(1))x_(n)` is

Prove that : (vi) log_(a)x + log_(a^2)x^(2) + log_(a^3)x^(3) + ………….+ log_(a^n)x^(n) = log_(a)x^(n)

If x=prod_(n=1)^(2000)n , then the value of the expression, 1/(1/((log)_2x)+1/((log)_3x)++1/((log)_(2000)x))i s dot

If x=prod_(n=1)^(2000)n, then the value of the expression, (1)/((1)/(log_(2)x)+(1)/(log_(3)x)+.........+(1)/(log_(2000)x))is..........

The coeffiecient of x^(n) in the expansion of log_(n)(1+x) is

The coefficient of x^(n) in the expansion of log_(a)(1+x) is

The coefficient of x^(n) in the expansion of log_(a)(1+x) is

If x=prod_(n=1)^(2000)n, then the value of expression,((1)/((log_(2)x))+((1)/(log_(3)x))+...............+((1)/(log_(2000)x)) (A) 2(B)3(C)1((1)/(log_(3)x))+............+((1)/(log_(2000)x))

If x_n > x_(n-1) > ..........> x_3 > x_1 > 1. then the value of log_(x_1) [log_(x _2) {log_(x_3).........log_(x_n) (x_n)^(x_(r=i))}]